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arXiv · 1201.2280

Non-smooth atomic decompositions, traces on Lipschitz domains, and pointwise multipliers in function spaces

Cornelia Schneider·Jan Vybíral
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Abstract

We provide non-smooth atomic decompositions for Besov spaces $\Bd(\rn)$, $s>0$, $0<p,q\leq \infty$, defined via differences. The results are used to compute the trace of Besov spaces on the boundary $Γ$ of bounded Lipschitz domains $Ω$ with smoothness $s$ restricted to $0<s<1$ and no further restrictions on the parameters $p,q$. We conclude with some more applications in terms of pointwise multipliers.

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Cornelia Schneider, Jan Vybíral. 2012-01-11. Non-smooth atomic decompositions, traces on Lipschitz domains, and pointwise multipliers in function spaces. https://arxiv.org/abs/1201.2280

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